Optimal control of a Bose-Eintein Condensate in an optical lattice: The non-linear and two-dimensional cases

TL;DR

This paper develops advanced optimal control algorithms for manipulating Bose-Einstein condensates in optical lattices, extending existing methods to non-linear and two-dimensional cases, enabling precise state preparation.

Contribution

It introduces generalized gradient-based algorithms derived from Pontryagin's maximum principle for non-linear and 2D Bose-Einstein condensate control.

Findings

High-precision target state achievement through laser phase adjustments

Extension of GRAPE algorithm to non-linear and 2D systems

Discussion of physical relevance and future research directions

Abstract

We numerically study the optimal control of an atomic Bose-Einstein condensate in an optical lattice. We present two generalizations of the gradient-based algorithm, GRAPE, in the non-linear case and for a two-dimensional lattice. We show how to construct such algorithms from Pontryagin's maximum principle. A wide variety of target states can be achieved with high precision by varying only the laser phases setting the lattice position. We discuss the physical relevance of the different results and the future directions of this work.